scholarly journals Equilibrium configurations of two charged masses in general relativity

2007 ◽  
Vol 76 (2) ◽  
Author(s):  
G. A. Alekseev ◽  
V. A. Belinski
Keyword(s):  
General Relativity ◽  
Equilibrium Configurations ◽  
Charged Masses

A note on the electrostatic equilibrium of charged masses in general relativity

1999 ◽  
Vol 17 (1) ◽  
pp. 251-252
Author(s):  
G P Perry ◽  
F I Cooperstock
Keyword(s):  
General Relativity ◽  
Electrostatic Equilibrium ◽  
Charged Masses

On the equilibrium of charged masses in general relativity: II. The stationary electrovacuum case

1999 ◽  
Vol 16 (11) ◽  
pp. 3725-3734 ◽  
Author(s):  
Nora Bretón ◽  
Vladimir S Manko ◽  
J Aguilar Sánchez
Keyword(s):  
General Relativity ◽  
Charged Masses

Equilibrium configurations of white dwarfs in the pseudo-complex general relativity

2017 ◽  
Vol 338 (9-10) ◽  
pp. 1085-1089 ◽  
Author(s):  
J. E. S. Costa ◽  
D. Hadjimichef ◽  
M. V. T. Machado ◽  
F. Köpp ◽  
G. L. Volkmer ◽  
...  
Keyword(s):  
General Relativity ◽  
White Dwarfs ◽  
Equilibrium Configurations ◽  
Complex General Relativity

scholarly journals BAROTROPIC THIN SHELLS WITH LINEAR EOS AS MODELS OF STARS AND CIRCUMSTELLAR SHELLS IN GENERAL RELATIVITY

1999 ◽  
Vol 08 (04) ◽  
pp. 549-555 ◽  
Author(s):  
KONSTANTIN G. ZLOSHCHASTIEV
Keyword(s):  
General Relativity ◽  
Equation Of State ◽  
Equations Of Motion ◽  
Thin Shells ◽  
Spherically Symmetric ◽  
Equilibrium Configurations ◽  
Barotropic Fluids ◽  
Circumstellar Shells ◽  
Relativistic Models ◽  
The Stability

The spherically symmetric thin shells of the barotropic fluids with the linear equation of state are considered within the frameworks of general relativity. We study several aspects of the shells as completely relativistic models of stars, first of all the neutron stars and white dwarfs, and circumstellar shells. The exact equations of motion of the shells are obtained. Also we calculate the parameters of the equilibrium configurations, including the radii of static shells. Finally, we study the stability of the equilibrium shells against radial perturbations.

The equilibrium of two charged masses in general relativity

1981 ◽  
Vol 83 (9) ◽  
pp. 414-416 ◽  
Author(s):  
W.B. Bonnor
Keyword(s):  
General Relativity ◽  
Charged Masses

Rotating massive stars in general relativity

1967 ◽  
Vol 296 (1445) ◽  
pp. 189-200 ◽  
Keyword(s):  
General Relativity ◽  
Stability Analysis ◽  
Simple Formula ◽  
Massive Star ◽  
Massive Stars ◽  
Rotation Velocity ◽  
Weak Field ◽  
Slow Rotation ◽  
Equilibrium Configurations ◽  
Schwarzschild Radius

Equilibrium models of uniformly rotating massive stars are investigated, using a weak field, slow rotation approximation, which is shown to be adequate for all cases of interest. The fate of radial perturbations about these equilibrium configurations is investigated using a linear­ized stability analysis to determine the oscillation frequency σ in a peturbation ∝ e iσ t . An eigenvalue equation for σ 2 is obtained which can be made self adjoint with respect to the spatial metric, and a variational principle to determine σ 2 is derived. Numerical determinations of σ 2 have been carried out for a variety of masses, radii and rotational velocities, and these results are incorporated in a simple formula that gives the dependence of σ 2 on these quantities. The condition for instability, σ 2 negative, is determined, and it is found that for large masses and maximum rotation velocity, so that when centrifugal force balances gravity at the surface, a massive star becomes unstable when its radius is 208 times the Schwarzschild radius 2 GM/c 2 .

scholarly journals NECESSARY AND SUFFICIENT CONDITION FOR HYDROSTATIC EQUILIBRIUM IN GENERAL RELATIVITY

2007 ◽  
Vol 16 (01) ◽  
pp. 35-52 ◽  
Author(s):  
P. S. NEGI
Keyword(s):  
General Relativity ◽  
Variational Method ◽  
Upper Bound ◽  
Trial Function ◽  
Hydrostatic Equilibrium ◽  
Dynamical Stability ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Equilibrium Configurations ◽  
Necessary And Sufficient

We present explicit examples to show that the "compatibility criterion" (recently obtained by us toward providing equilibrium configurations compatible with the structure of general relativity) which states that for a given value of σ[≡ (P0/E0) ≡ the ratio of central pressure to central energy-density], the compactness ratio u[≡ (M/R), where M is the total mass and R is the radius of the configuration] of any static configuration cannot exceed the compactness ratio, uh, of the homogeneous density sphere (i.e., u ≤ uh) is capable of providing a necessary and sufficient condition for any regular configuration to be compatible with the state of hydrostatic equilibrium. This conclusion is drawn on the basis of the finding that the M–R relation gives the necessary and sufficient condition for dynamical stability of equilibrium configurations only when the compatibility criterion for these configurations is appropriately satisfied. In this regard, we construct an appropriate sequence composed of core-envelope models on the basis of compatibility criterion such that each member of this sequence satisfies the extreme case of causality condition v = c = 1 at the center. The maximum stable value of u ≃ 0.3389 (which occurs for the model corresponding to the maximum value of mass in the mass–radius relation) and the corresponding central value of the local adiabatic index, (Γ1)0 ≃ 2.5911, of this model are found fully consistent with those of the corresponding absolute values, u max ≤ 0.3406 and (Γ1)0 ≤ 2.5946, which impose strong constraints on these parameters of such models. In addition to this example, we also study dynamical stability of pure adiabatic polytropic configurations on the basis of variational method for the choice of the "trial function," ξ = reν/4, as well as the mass–central density relation, since the compatibility criterion is appropriately satisfied for these models. The results of this example provide additional proof in favor of the statement regarding compatibility criterion mentioned above. Together with other results, this study also confirms the previous claim that just the choice of the "trial function," ξ = reν/4, is capable of providing the necessary and sufficient condition for dynamical stability of a mass on the basis of variational method. Obviously, the upper bound on the compactness ratio of neutron stars, u ≅ 0.3389, which belongs to two-density model studied here, turns out to be much stronger than the corresponding "absolute" upper bound mentioned in the literature.

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